Probably a jumbled up recollection of the pirated plays people would scribble down to sell to printers or to competing theatre companies.

The First Folio and other “good” sources were probably not directly from Shakespeare’s drafts either, but from revised working scripts that the King’s Men had around. Still a vast jump from there to “weren’t written down until later.”

In general, there’s a lot of needless mystery and “bardolatry” surrounding Shakespeare, when in fact he was reasonably well documented for a commoner, has had every single scrap of evidence for his life and career scoured over a dozen times, had works of uneven quality, and most of what’s unique about him jibes perfectly well with a half-educated prodigy coming in from the country and working in a milieu that was kind of edgy and open to experimentation.